Decomposition of the nodal conductance matrix of a planar resistive grid and derivation of its eigenvalues and eigenvectors using the kronecker product and sum with application to cnn image filters
Künye
Tavşanoğlu, A. V. (2016). Decomposition of the nodal conductance matrix of a planar resistive grid and derivation of its eigenvalues and eigenvectors using the kronecker product and sum with application to CNN image filters. IEEE Transactions on Circuits and Systems I: Regular Papers, 63(12), 2169-2179. doi:10.1109/TCSI.2016.2617918Özet
It is shown that an (M× N)-node planar resistive grid can be decomposed into two sub-grids; one made up of M N-node horizontal and the other of N M-node vertical linear resistive grids which corresponds to decomposing its nodal conductance matrix (NCM) into the Kronecker sum of the NCMs of horizontal and vertical linear grids. This enables the analytical expressions of the eigenvalues and eigenvectors of the NCMs of the sub-grids as well as those of the planar resistive grid to be expressed in terms of those of the two linear grids, whose analytical expressions are well known. For a Cellular Neural Network (CNN) Gabor-type filter (GTF) we define generalized nodal conductance matrices (GNCMs) that correspond to the NCMs of the resistive sub-grids, show that each Kronecker decomposition has a counterpart in CNN GTF and prove that each GNCM, its counterpart NCM and the corresponding temporal state matrices are related through unitary diagonal similarity transformations. Consequently, we prove that the eigenvalues of the temporal state matrix of a spatial band-pass CNN GTF are the same as those of its counterpart spatial low-pass CNN image filter, hence their temporal transient behaviors are similar in settling to a forced response.
Kaynak
IEEE Transactions on Circuits and Systems I: Regular PapersCilt
63Sayı
12İlgili Öğeler
Başlık, yazar, küratör ve konuya göre gösterilen ilgili öğeler.
-
Gerçel ve karmaşık süzgeç öbeklerinin eşdalgacıklı tasarımı
Ateş, Hasan Fehmi; Orchard, Michael T.; Kanberoğlu, Berkay (IEEE, 2006-07-31)Bu bildiride, eşdalgacıklı tam geri çatma süzgeç öbekleri tasarlamak için, Parks-McClellan algoritması gibi tekniklerle üretilen enküçük-enbüyük optimal eşdalgacıklı kısıtsız süzgeçleri eşlemlemede kullanılan basit bir ... -
SRFT ile frekans transformasyonunu kullanarak band geçiren filtre prototipi üzerinden çokluband filtre tasarımı
Yıldız, Serkan; Aksen, Ahmet; Yarman, Bekir Sıddık Binboğa (IEEE, 2017-02-10)Çokluband filtre tasarım problemi analitik ve uygulama yönünden ele alınr. Temel amaç Almaç Güç Kazanç (AGK) karakteristiğini frekans band üzerinden tanımlamaktır. AGK’nın belli bantlarda yükseltilmesi belli bantlarda ... -
Design and realization of 8-12 GHz cascaded unit element microstrip filter for X-band
Köprü, Ramazan; Atilla, Doğu Çağdaş; Aydın, Çağatay; Kılınç, Sedat; Yarman, Bekir Sıddık Binboğa (IEEE, 2016)Design of a wideband cascaded unit element microstrip bandpass filter (UEBPF) operating along the whole X-band (8-12 GHz) is presented with satisfactory agreement between theoretical and measurement results. Simplified ...